Answers
The missing statement and the reason of LN bisects ∠MLO, LM≅LO are given and ∠OLN≅∠MLO is because of definition of angle bisector, LN≅LN is because it is common to both the angles ∠LNO AND ∠LNM, LO≅LM is because ΔLNO and ΔLNM both are congruent.
Given that:
LN bisects ∠MLO and LM≅LO
Prove that: ΔLMN ≅ ΔLON
In order to prove ASA congruence between the triangles we need two angles to be congruent to each other. When we look at the figure, we see that ∠LNO ≅ ∠LNM is a common angle in both the triangles.
Hence, using this we will prove that the triangles are congruent by ASA congruence rule.
In ΔLON and ΔLMN
Side ON ≅ Side MN
∠LNO ≅ ∠LNM ( ∵ common angle)
∠ONL ≅ ∠MNL (∵ Given as LN is the angle bisector of ∠MLO)
⇒ ΔLMN ≅ ΔLON ( By ASA congruence theorem).
Statement 1: LN bisects ∠MLO
Reason: Given.
Statement 2: LM≅LO
Reason: Given.
Statement 3: ∠OLN≅∠MLO
Reason: Definition of angle bisector.
Definition of angle bisector: An angle bisector is defined as a line segment that bisects one of the vertex angles of a triangle.
Statement 4: LN≅LN
Reason: Common to both the angles ∠LNO AND ∠LNM and also these angles are 90° because angle made by angle bisector is always 90°.
Statement 5: LO≅LM
Reason: ΔLNO and ΔLNM both are congruent.
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Related Questions
Find the midpoint of the line segment with end coordinates of:
(0, 2) and (8,8)
Answers
The mid point of the line segment with the end coordinates of:
(0, 2) and (8,8) is (4,5).
Define the term mid point?A mathematical expression known as the midpoint formula is used to determine where two data points meet midway. This formula is also used in the study of economics to determine this same coefficient of elasticity, etc.The midpoint is the point on the center of the line that is equally distant as from 2 points if a line is created connecting the two points.For the given question;
The given coordinates are-
(x1, y1) = (0, 2)
(x2, y2) = (8,8)
The mid point is found by the formula;
x = (x1 + x2 )/2
y = (y1 + y2)/2
Put teh values,
x = (0 + 8)/2
x = 4
y = (2 + 8)/2
y = 5
Thus, the mid point of the line segment with the end coordinates of:
(0, 2) and (8,8) is (4,5).
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3 to the second power times 3 to the third power
Answers
PLEASE HELP ASAP!!! Find the volume of a cube with the given side length.
1/5b^3
Answers
The volume of the cube is 1/125b⁹
How to determine the volume of the cube?From the question, we understand that
Shape = Cube
Side length = 1/5b³
Rewrite the side length as
a = 1/5b³
The volume of a cube can be expressed as V = a³
where a is the length of any side
And v is the volume
Substitute the known values in the above equation So, we have the following equation
V = (1/5b³)³
Evaluate
V = 1/125b⁹
Hence, the volume is V = 1/125b⁹
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Solve the equation 32 = v + 27 for v.
−5
5
−59
59
Answers
Answer:
Step-by-step explanation: 32=v + 27
V= 5
how:
32-27=5
v=5
I don"t know what you meant for at the bottom, if that is included please explain what you mean.
Answer:
5
Step-by-step explanation:
32 = v + 27
Subtract 27 from both sides and make v the subject.
32 - 27 = v
5 = v
The names or notes of all the white notes on a piano are written in pieces of paper and placed in a cup. There are 7 sets of the notes D E F and G and 8 sets of the notes A B and C. If a person draws one note out of the cup without looking what are the chances of them getting a c
Answers
The probability that the person obtains a note with C written in it is of:
0.1538 = 15.38%.
How to calculate a probability?The probability of an event in an experiment is obtained as the number of desired outcomes in the context of the experiment divided by the number of total outcomes in the context of the experiment.
The total number of notes in this problem is composed as follows:
7 notes of each of D, E, F and G.8 notes of each of A, B and C.Hence the total number is of:
Total = 7 x 4 + 8 x 3 = 52 notes.
The desired number of outcomes is the number of notes with C, hence:
Desired = 8 notes.
Thus the probability is calculated as follows:
Probability = Desired/Total = 8/52 = 0.1538 = 15.38%.
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2. Which expression represents the simplest form of xy + 3xy?
3xy
3x²y^2
4x²²
4xy
Answers
The simplest form is 4xy
From the question, we have
xy + 3xy = 4xy
The simplest form is 4xy.
Addition:
The act of combining two or more items is known as addition. The process of computing the sum of two or more numbers in mathematics is called addition. It is a fundamental mathematical procedure that is frequently used in daily life. When we work with money, figure out our food bills, or figure out the time, we frequently employ addition. One-digit numbers can be added simply for solving addition problems, however for bigger numbers, we divide the numbers into columns using their corresponding place values, such as ones, tens, hundreds, thousands, and so on.
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Let
U
be the universal set, where:
U
=
{
1
,
2
,
3
,
4
,
5
,
6
,
7
,
8
,
9
,
10
}
Let sets
A
and
B
be subsets of
U
, where:
A
=
{
4
,
8
,
9
,
10
}
and
B
=
{
2
,
3
,
4
,
6
,
7
}
Find
(
A
∩
B
)
c
:
{
}
Find
A
c
∪
B
c
:
{
}
Enter the elements as a list, separated by commas in order from smallest to largest. If the result is the empty set, enter DNE
Answers
The elements of set (AnB)' = {1,2,3,5,6,7,8,9,10} and The elements of A'uB' = {1,2,3,5,6,7,8,9,10}
What is complement of a set?The complement of a set is the set that includes all the elements of the universal set that are not present in the given set. For example, if A is a set of all coins which is a subset of a universal set that contains all coins and notes, so the complement of set A is a set of notes (which do not includes coins).
Therefore if U={1,2,3,5,6,7,8,9,10} and A={4,8,9,10} B= {2,3,4,6,7} then,
(AnB) = {4}
(AnB)' = {1,2,3,5,6,7,8,9,10}
A' = {1,2,3,5,6,7} and B' = {1,5,8,9,10}
therefore A'uB'= {1,2,3,5,6,7,8,9,10}
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To prepare for his mountain biking trip, Rhyan bought four tire patches. Rhyan paid using a gift card that had $22.20 on it. After the sale, Rhyan’s gift card had $1.90 remaining. Which equations could you use to find the price of one tire patch? Select all that apply. 4x – 1.9 = 22.2 4x – 22.2 = 1.9 4x + 1.9 = 22.2 4x + 22.2 = –1.9 22.2 – 4x = 1.9
Answers
The equations you use to find the price of one tire patch are 4x + 1.9 = 22.20 and 22.2 – 4x = 1.9, so options A and E are correct.
What is equation?A formula known as an equation uses the equals sign to denote the equality of two expressions.
Given:
The Balance on the gift card = $22.20,
The no of patches bought = 4,
The left balance on the card = $1.90.
The equation for the statement in the question is,
The no of patches bought × The price of patches + The left balance on the card = The Balance on the gift card
Let x be the price of one batch
Substitute the values,
4x + 1.9 = 22.20 or 22.2 – 4x = 1.9
Therefore, the equations you use to find the price of one tire patch are 4x + 1.9 = 22.20 and 22.2 – 4x = 1.9.
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How many more white squares are there than black squares in the 47th term? Explain how you know.
Expression (White Squares):
Expression: (Black Squares):
Answers
There are 9216 more white squares than black squares in the 47th term with it's an odd number of 97
How to calculate the 47th termThe terms are generated with the square of odd numbers with the black squares being the addition of the odd number and one subtracted from it.
For the 47th term:
Given that the first term is consists of 25 squares with 9 black and 16 white squares
first term has odd number 5
the square of 5; 5² = 25
black squares = 5 + (5-1) = 9
white squares = 25 - 9 = 16
Therefore, for the 47th term:
47th term has odd number 97
the square of 97; 97² = 9409
black squares = 97 + (97-1) = 193
white squares = 9409 - 193 = 9216
Hence, the 47th term has an odd number 97 with 9216 more black squares than the white squares,
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subtract -2x^2+5x+10 and -7x-3
Answers
The difference of the given algebraic expressions is -2x²+12x+13.
The given algebraic expressions are -2x²+5x+10 and -7x-3.
What is the subtraction of expressions?To subtract an algebraic expression from another, we should change the signs (from '+' to '-' or from '-' to '+') of all the terms of the expression which is to be subtracted and then the two expressions are added.
The subtraction of given expressions is as follows
-2x²+5x+10-(-7x-3)
= -2x²+5x+10+7x+3
= -2x²+12x+13
Hence, the difference of the given algebraic expressions is -2x²+12x+13.
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Let f(x) = 1 / 2+3x and point P = (2 , 1/8)
a.) Use the following definition of the slope of the tangent line at x = a to find the slope of the line tangent to the graph of f at P.
m = lim f(a+h) - f(a) / h
tan h --> 0
b.) Determine an equation of the tangent line at P.
Answers
The slope is -3/(2+3a)² and the equation of the line is y - 1/8 = [-3/(2+3a)²](x - 2).
What is the slope?The ratio that y increase as x increases is the slope of a line. The slope of a line reflects how steep it is, but how much y increases as x increases. Anywhere on the line, the slope stays unchanged (the same).
[tex]\rm m =\dfrac{y_2-y_1}{x_2-x_1}[/tex]
f(x) = 1 / 2+3x and point P = (2 , 1/8)
f(x+h) = 1/(2 + 3a + 3h)
f(a) = 1/(2 + 3a)
m(tan) = [1/(2 + 3a + 3h) - 1/(2 + 3a)]/h
After simplifying:
m(tan) = -3/[(2+3a)(2+3a+3h)]
h = 0
m(tan) = -3/(2+3a)²
The equation of the line:
y - 1/8 = [-3/(2+3a)²](x - 2)
Thus, the slope is -3/(2+3a)² and the equation of the line is y - 1/8 = [-3/(2+3a)²](x - 2).
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A square with sides length x are cut out of each corner of a rectangular piece of cardboard measuring 5ft by 8ft. The resulting piece of cardboard is then folded into a box without a lid. Find the volume of the largest box that can be formed this way.
Answers
The volume of the largest box that can be made from the rectangular cardboard obtained by using the value of the derivative of the function for the volume at the extremum point is 18 cubic feet
What is an extremum point in mathematics?An extremum of a function is the point where the value of the function is a maximum or a minimum.
The side length of the cut out squares = x
The width of the rectangular cardboard = 5 feet
The length of the rectangular cardboard = 8 feet
The length of the side of the cut square = 8 - 2·x
Width of the side of the cut square = 5 - 2·x
Height of the cut square = x
Volume of the cut square, V = (8 - 2·x) × (5 - 2·x) × x = 4·x³ - 26·x² + 40·x
When the volume of the box is largest, we have;[tex]V' = \dfrac{d}{dx} \left(4\cdot x^3 - 26\cdot x^2 + 40\cdot x\right) = 12\cdot x^2 - 52\cdot x + 40=0[/tex]
12·x² - 52·x + 40 = 0
3·x² - 13·x + 10 = 0
Which gives;
(3·x - 10)·(x - 1) = 0
The dimensions of the cut square that gives the maximum volume are therefore;
x = 1 or x = 10/3
When x = 10/3, we have;
V = (8 - 2×(10/3)) × (5 - 2×(10/3)) × (10/3) ≈ -200/27 < 0
When x = 1, we have;
V = (8 - 2×1) × (5 - 2×1) × 1 = 18
The value of x that gives the maximum volume is therefore, x = 1
The dimensions of the box that give the maximum volume are therefore;
Height = x = 1
Length = 8 - 2×1 = 6
Width = 5 - 2 × 1 = 3
The dimensions of the box that gives the maximum volume are;
Height = 1 ft
Length = 6 ft
Width = 3 ft
The volume of the largest box that can be formed is 18 cubic feet
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compare 5.9 and 152 using <, > or =
Answers
Answer:
Step-by-step explanation:
HELP PLS AND HURRY!!!
Answers
Answer:
1. 5√7
2. (√15)/6
Step-by-step explanation:
1. √175
= √(25) * √(7)
= 5√7
2. √(5/12)
= (√5)/(√12)
= (√5)/(√(4) * √(3))
= (√5)/(2√3)
Radicals can't be in the denominator:
(√5)/(2√3)
(√5 * 2√3)/(2√3 * 2√3)
(2√15)/12
(√15)/6
1. Find the y-intercept of the line passing through the points A (3, -2) and B (-1, 3). (5 pts)
Answers
Answer:
-1.25
Step-by-step explanation:
m=
[tex]y2 - y1 \div x2 - x1[/tex]
3- (-2)÷ -1-3
5/-4
m=-1.25
An investment portfolio is shown below.
Investment Amount Invested ROR
Savings Account $3,200 2.1%
Municipal Bond $4,900 4.5%
Preferred Stock $940 10.5%
Common Stock A $1,675 −3.5%
Using technology, calculate the weighted dollar amount of the savings account.
−$58.63
$58.63
−$67.20
$67.20
Answers
The weighted dollar amount of the savings account as per the an investment portfolio is; $67.20.
What is the percentage?A percentage is a minimum number or ratio that is measured by a fraction of 100.
Given that An investment portfolio is;
Investment Amount Invested ROR
Savings Account $3,200 2.1%
Municipal Bond $4,900 4.5%
Preferred Stock $940 10.5%
Common Stock A $1,675 -3.5%
The weighted dollar amount of the savings account is;
= 2.1% of $3200
= ( 2.1 / 100) × $3200
= ($6720) /100
= $ 67.20
Therefore, the weighted dollar amount of the savings account as per the an investment portfolio is; $67.20.
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Assume the radius of a certain planet is 4790 km and the planet is a sphere. What is its surface area?
Answers
Answer:
A ≈ 2.88×108km²
Step-by-step explanation:
A= 4 π r² = 4·π· 47902 ≈ 2.88324×10 power 8 km²
Given the equation F=95C+32 where C is the temperature in degrees Celsius and F is the corresponding temperature in degrees Fahrenheit, and the following ordered pairs:
(25,F1), (−30,F2)
Answers
The corresponding values of F1 and F2 in the ordered pairs are 77 degrees Fahrenheit and -22 degrees Fahrenheit
How to use the equation to convert from degrees Celsius to degrees Fahrenheit?
Given: the equation F=9/5C+32 and ordered pairs: (25, F1), (−30, F2)
In order to convert the given values to degrees Fahrenheit, substitute the given values into the equation to get F1 and F2 respectively:
For (25, F1):
F = 9/5 C+32 (put C= 25 in the equation)
F1 = 9/5(25) + 32
F1 = 45 +22
F1 = 77 degrees Fahrenheit
For (−30, F2):
F = 9/5 C+32 (put C= -30 in the equation)
F2 = 9/5(-30) + 32
F2 = -54 + 32
F2 = -22 degrees Fahrenheit
Therefore, the values of F1 and F2 are 77 degrees Fahrenheit and -22 degrees Fahrenheit respectively
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To find the local extrema of a polynomial function f(x) = anxn + an-1xn-1 + … + a2x2 + a1x + a0 (or any other function), you would apply the equation f ’(x) = 0. Consider the basic form of a quadratic equation: f(x) = ax2 + bx + c. Apply the equation above to this quadratic function and solve for x. The resulting equation should be familiar from algebra/pre-calculus. What did you call this equation and how is it related to the location of a local extrema on a quadratic function?
Answers
The resulting equation is the x-coordinate of the point of local extrema of a quadratic function.
To find the local extrema of a polynomial function f(x), we apply the equation f'(x) = 0. We are given the basic form of a quadratic equation. The equation is given below.
f(x) = ax² + bx + c
We need to find the differentiation of the above equation.
f'(x) = 2ax + b
Now, we will equate the obtained equation to zero and solve for the value of the variable "x".
f'(x) = 0
2ax + b = 0
2ax = -b
x = -b/2a
This resulting equation is familiar from algebra/pre-calculus. This is the x-coordinate of the point of local extrema of a quadratic function.
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Two beetles sit at the top edge of the house roof. The roof has two faces. The first face is such that the horizontal shift by 3 cm along this face means 2 cm shift vertically. Simultaneously the beetles start moving downwards, the first beetle by the first face, the second – by the second face of the roof. First beetle moves twice as fast as the second beetle. Find the altitude of the second beetle above the first beetle when they will be 72 cm apart horizontally, if the second face of the roof
has the same incline as the first face.
Answers
Answer:
I 728.Two beetles sit at the verticesAandHof a cubeABCDEFGHwith edge length40√110 units. The beetles start moving simultaneously alongACandHFwiththe speed of the first beetle twice that of the other one.....ADCBEFGH✈s✈s. . . . . . . . . . . . . . . . . . . . . . . . ......................................................................What will be the shortest distance between the beetles?29.In the diagram,4PQRhas an area of 960 square units. The pointsS,TandUare the midpoints of the sidesQR,RPandPQ, respectively, and the linesPS,QTandRUintersect atW.......PQRSUTNMLW✓✓✼. . . . . . . . . . . . . . .....................The pointsL,MandNlie onPS,QTandRU, respectively, such thatPL:LS= 1 : 1,QM:MT= 1 : 2 andRN:NU= 5 : 4.What is the area, in square units, of4LMN?30.A 40×40 white square is divided into 1×1 squares by lines parallel to its sides.Some of these 1×1 squares are coloured red so that each of the 1×1 squares,regardless of whether it is coloured red or not, shares a side with at most one redsquare (not counting itself). What is the largest possible number of red squares?
Step-by-step explanation:
Answer:
16
Step-by-step explanation:
I need help in answering this question
Answers
Answer:
2 6 12 20,000
6 18 36 60,000
Step-by-step explanation:
The bottom number is 3 times the top number.
Which is the graph of y = 3¥x+2 + 3?
Answers
The graph of the equation y = 3x + 2 + 3 is shown below .
In the question ,
it is given that ,
the equation of the line is y [tex]=[/tex] 3x [tex]+[/tex] 2 [tex]+[/tex] 3 ,
we need to draw the graph of it .
Do draw the graph we need at least two points .
for the first point
put x = 0
we get ,
y = 3(0) + 2 + 3
y = 0 + 2 + 3
y = 2 + 3
y = 5
the first point is (0,5)
for the second point put y = 0,
we get ,
0 = 3x + 2 + 3
3x = - 2 - 3
3x = -5
x = -5/3 ,
So , the second point is (-5/3 , 0)
the graph of the given equation is shown below .
Therefore , The graph of the equation y [tex]=[/tex] 3x + 2 [tex]+[/tex] 3 is shown below .
The given question is incomplete , the complete question is
What is the graph of the equation y = 3x + 2 + 3 ?
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what is the volume of the recycling box shown in the diagram , 20cm, 40cm, 60cm can someone please help asap
write answers and working out.
Answers
Answer:
i got 48000
Step-by-step explanation:
20x40x60
when solving volume you multiply the length times width times height.
Okay I think I'm going on to see if ur in
Answers
Answer:
21y-7/11
Step-by-step explanation:
First you would multiply everything outside of the prhthises to the inside. Second multiply 7 times 3y that would equal 21y. Third multiply 7 times - 1/11 that would equal to 21y-7/11
on the coordinate plane, the number line that runs right and left is the?
A: x-coordinate
B: y-coordinate
C: x-axis
D: y-axis
Answers
Answer:
C: x-axis
Step-by-step explanation:
It is the x-axis.
Find the image vertices for a dilation with center (0,0) and a scale factor of 4.
Answers
After dilation with center (0, 0) and scale factor 4 the required image vertices of the given image is given by A' =(-12 , 4), B' =(16 , -12),
C' = (8 , 12), D' = (-4 , 16).
As given in the question,
From the given graph of quadrilateral the vertices of the given image is given by :
A and D are second quadrant , C is first quadrant and B is in fourth quadrant.
Each unit on both the axis represents 1 unit only.
Coordinates of each vertices are:
A = (-3 , 1) , B = (4 , -3) ,C = (2 , 3), D = (-1 , 4)
Now for dilation scale factor is equal to 4
Image vertices for a dilation with center (0 , 0) multiply the vertices by scale factor 4.
Required image vertices are given by:
A' = (-12 , 4),
B' = (16 , -12)
C' = (8 , 12)
D' = (-4 , 16)
Therefore, after dilation with center (0, 0) and scale factor 4 the required image vertices of the given image is given by A' =(-12 , 4), B' =(16 , -12),
C' = (8 , 12), D' = (-4 , 16).
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Determine the x- and y-intercepts of the graph of x+2y=−4 .
Then plot the intercepts to graph the equation.
Keyboard Instructions
Initial graph state
The horizontal axis goes from -10.8 to 10.8 with ticks spaced every 1 unit(s).
The vertical axis goes from -10.8 to 10.8 with ticks spaced every 1 unit(s).
Answers
Answer:
Step-by-step explanation:
1) first we find the x and y intercepts. Remember the intercepts are where x=0 and y=0
2) To find the x-intercept, substitute y = 0 and solve for x.
given equation: x +2y= -4
then substitute y=0 so
x+ 2(0) = -4 -> any number multiplied by 0 it will always equal zero
then, it will be x=-4
the coordinates will be (-4,0)
3) To find the y-intercept, substitute x =0 and solve for y.
given equation: x +2y= -4
then substitute x=0 so
(0)+ 2y = -4 -> x disappears since is zero
then, it will be 2y=-4
then we multiply by 2 :
2y/2 = -4/2
y=-2
the coordinates for the y-intercept will be (0,-2)
graph:
Darren planted sunflowers in the community garden. During his last visit to the garden, the plants were 60 inches tall. Today, Darren found them to be 10% taller. How tall are the sunflowers now?
please due tommroe
Answers
Answer:
66 inches
Step-by-step explanation:
60 + .1(60)
60 + 6
66
Answer:
66 inches
Step-by-step explanation:
60 x .10 = 6
60 +6 =66
need help, preferably with solution
Answers
By evaluating f(x) in x = 0 we will see that the value is 1, then we will get:
f²⁰²³(0) = 1²⁰²³ = 1
How to evaluate the expression?Remember that 1 is the identity of the multiplication, this means that any number times 1, is equal to the same number.
Then, for any real value n, we know that:
1ⁿ = 1
Now we have the function:
f(x) = 1/(1 + x²)
Evaluating in x = 0, we get:
f(0) = 1/(1 + 0²) = 1
Now we can apply the exponent n = 2023 we will get:
f²⁰²³(0) = 1²⁰²³ = 1
The answer is 1.
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John worked 18 hours last week. He earned $216. What was his hourly rate?
Answers
Divide $216 by 18 to get $12